It does have that through portals:
https://github.com/flatpak/xdg-desktop-portal
If you Flatpak a Gtk+ 3 or modern Qt application you get portals for free. E.g. I packaged a Qt application and I am not sharing the home directory - when the user opens a file it uses the Qt/KDE portal (similarly to macOS, ChromeOS, etc.).
As far as I understand the problem is that portals are only available for Gtk+ and recent Qt versions. Some of the applications that the posts mentions use toolkits that probably don't support portals (Java JDK, wxWidgets, etc.).
The situation for Linux is a bit different than e.g. macOS, where practically everything uses Cocoa and Apple could just throw the switch.
So, for applications that do not use vanilla Gtk+ or Qt they still need to make the home directory visible or they would not be Flatpack'able.